TOKYO — The past three weeks may have been the toughest of Moon Jae-in’s presidency. The centerpiece of the South Korean leader’s rule, rapprochement with North Korea, is in tatters after the breakdown of the summit between President Trump and North Korean leader Kim Jong Un.

Opinion polls released this past week show his popularity falling to its lowest level since his inauguration nearly two years ago, while on Friday, North Korea threatened to pull out of negotiations with the United States entirely if Washington didn’t drop its “gangster-like” demands.

Hours after the Hanoi summit broke down, Trump spoke to Moon by telephone and asked him to “play an active role as a mediator” by talking to Kim, South Korea’s presidential Blue House said.

But if Moon’s skills as mediator have perhaps never been more in demand, his credibility as a neutral intermediary have seldom been more questioned.

In the National Assembly last week, conservative opposition leader Na Kyung-won caused a furor by suggesting that Moon was embarrassing the nation by acting as “the chief spokesman of Kim Jong Un.”

But the attacks have come not just from his domestic political foes, but also from Washington and the United Nations.

Moon, a former human rights lawyer, has faced persistent criticism for downplaying North Korea’s abysmal human rights record in the interests of the peace process. On Thursday, the U.S. State Department said his government had put “direct and indirect” pressure on North Korean defector organizations to reduce their criticism of North Korea.

“This pressure allegedly included, for example, the termination of 20 years’ funding support for the Association of North Korean defectors in December 2017, police blocking groups’ efforts to send leaflets into North Korea by balloon, and police visits to organizations and requests for information on financial and other administrative matters,” the State Department wrote in its annual human rights report.

North Korean refugees were also reportedly asked “not to participate in public-speaking engagements that might be perceived as critical of the Moon administration’s engagement with North Korea,” the report said.

Earlier in the week, a report by a U.N. panel of experts said Seoul should have informed the United Nations of the transfer of more than 300 tons of petroleum products to North Korea in 2018.

Although the transfers were made to support inter-Korean engagement projects and were of no “economic value” to North Korea, the transaction should still have been reported to the United Nations’ sanctions committee, the report said, in what was an embarrassing oversight for a key U.S. ally.

Moon has also been criticized for cozying up to Kim and failing to ask him tough questions — for example, about how Kim defines denuclearization — so as not to upset the talks process.

But it seems that his efforts have not been entirely appreciated in Pyongyang, either.

On Friday, North Korea’s vice foreign minister, Choe Son Hui, described South Korea as “a player, not an arbiter” because it is an ally of Washington, the Associated Press reported.

To some extent, that’s a reflection of the difficult job Moon ­faces.

“A South Korean progressive mediating between a Republican president and North Korean communists — that’s not easy,” said John Delury, an associate professor at Yonsei University in Seoul.

Delury says there is no obvious next move for Trump and Kim, with neither wanting to lose face and both having to deal with hard-liners at home. In that sense, Moon might have the best hope of unlocking the impasse, perhaps by inviting Kim to visit Seoul, he argues.

“I’m not overflowing with optimism, but he’ll try” to mediate, Delury said. “Who else will get Kim Jong Un back into play? They do seem to have a good relationship, and some level of trust is there.”

Others are more skeptical.

North Korea’s uncompromising behavior in recent weeks partly reflects the limits of Moon’s capacity to mediate, said Christopher Green, senior adviser for the Korean Peninsula at the International Crisis Group. That means “the praise heaped upon his diplomatic skill in 2018 was somewhat misplaced,” he said.

With Moon’s reputation staked so heavily to the peace process, it is not surprising to see the impasse reflected in public opinion.

The Realmeter polling agency said the drop in Moon’s approval rating, to 45 percent, was partly attributable to growing skepticism over North Korea’s commitment to denuclearization after the failure of the Hanoi summit.

There have also been persistent reports of tensions between Seoul and Washington over Moon’s enthusiasm for fostering closer economic ties with North Korea, despite the lack of progress toward denuclearization.

Chun Yung-woo, a South Korean conservative who represented his country in talks over North Korea’s nuclear program from 2006 to 2007, says Moon now needs to prove he is able not just to convey U.S. positions to Kim, but also to have a “candid discussion” and persuade Kim to do what needs to be done to get the dialogue process back on track.

“If Washington believes President Moon and his administration are blind, and are only interested in marketing North Korea’s position, that their goal is to resume inter-Korean economic projects even at the expense of denuclearization — in short, if President Trump believes President Moon is on North Korea’s side — his role as a moderator will be constrained,” Chun said.

Tong Zhao, a fellow at the ­Carnegie-Tsinghua Center for Global Policy in Beijing, said it was “increasingly puzzling” to figure out what Moon really thinks — whether he really believes that Kim is willing to denuclearize, or is just playing along with the idea to achieve his own goal, ending the war that is technically not yet ended on the Korean Peninsula.

Tong and others appear increasingly doubtful that Moon’s confidence-building approach is still the best way forward.

“We have a lot of things going on and somebody has to take the helm, but I’m not sure that South Korea’s approach, which is continue with inter-Korean economic engagement, is the right answer,” said Jung H. Pak, a senior fellow at the Brookings Institution’s Center for East Asia Policy Studies.